# Frequency Response of R-C network

20/07/2013 12:59

Author Name:                              Leandrou Vasilis

OBJECTIVES

This report aims to:

• Notice the result of frequency on the impedance of a series R-C network.
• Plot the voltages and the flow of electricity of a series R-C network against frequency.
• Find out and make a diagram with the phase angle of the input impedance against frequency.

BACKGROUND THEORY

In this experiment will be used a DMM, an Oscilloscope, a function generator, 1KΩ resistor and 0.1μF capacitor.

• The DMM read resistance, voltage and current with a digital display.
• The oscilloscope is an instrument that will display the variation of a voltage with time on a flat screen monitor.
• A function generator typically expands on the skills of the audio oscillator by supplying a square wave and triangular waveform with an increased frequency range.
• Capacitor is an element constructed simply of two surfaces separated by the air gap. The capacitor displays its true characteristics only when a change in the voltage or current is made in the network.

EQUIPMENT

·         Digital Multimeter                  (Brand: Good Will Instruments Co. Ltd, Model: GDM-8135, Serial Number: CF-922334)

·         Dual Trace Oscilloscope         (Brand: HAMEG, Model: HM 203-6, Serial Number: 46/87 Z33418)

·         Function generator                  (Model: TG 550)

·         One 1KΩ resistor

·         One 0.1μF Capacitor

EXPERIMENTAL METHOD AND PROCEDURE

Part 1

The function generator was connected in series with the 1KΩ resistor and the 0.1μ capacitor. The oscilloscope was connected on the capacitor. The voltage across the capacitor was measure in deferent values of frequency (table 1). Then the resistor interchanges position with the capacitor. The voltage across the resistor was measured in different values of frequency (table 1). The current of the series circuit was calculated (table 1). Then the input voltage was set on 4V. The ZT was calculated using two different formulas (table 2). The angle θ was calculated (table 3).

OBSERVATIONS

 Frequency(kHz) Vc(p-p) (V) VR(p-p) (V) Ip-p (mA) 0.1 4 0 0 0.2 4 0.3 302.7μA 0.5 3.8 1.3 1.31 1 3.4 2.2 2.21 2 2.2 3 3.02 4 1.8 3.6 3.63 6 1 3.8 3.83 8 0.8 3.8 3.83 10 0.3 3.8 3.83

Table 1 Vc, VR, I versus Frequency.

 Frequency(kHz) Ep-p (V) Ip-p (mA) ZT=Ep-p/Ip-p (KΩ) ZT=  RxR+XcxXc (kΩ) 0.1 4 0 oo oo 0.2 4 302.7μA 13.21 13.24 0.5 4 1.31 3.05 3.06 1 4 2.21 1.8 1.79 2 4 3.02 1.32 1.29 4 4 3.63 1.1 1.1 6 4 3.83 1.04 1.02 8 4 3.83 1.04 1.02 10 4 3.83 1.04 0.99

Table 3 θ versus frequency.

 Frequency(kHz) R(measure) (Ω) Xc (KΩ) θ= -tan (Χc/R) 0.1 991 oo 0.2 991 13.21 -85.7 0.5 991 2.9 -71.1 1 991 1.54 -57.2 2 991 0.729 -36.3 6 991 0.261 -14.76 10 991 0.078 -4.5

Data discussion

The voltage across the capacitor becomes shorter with increasing frequency since the capacitive reactance is inversely proportional to the applied frequency. On the table 1 seeing that when f= 0.1 kHz Vc= 4V and when the f= 4 kHz Vc=1.8v.

Since the voltage and current of the resistor continue to be related by the fixed resistant value, the shapes of their curves versus frequency will have the same characteristics.

The voltages across the element an ac circuit are rector-ally related otherwise, the voltage readings may appear to be totally incorrect and not satisfy KVL.

On the table 1 seeing that as the frequency increases the voltage across the resistor and the current increases. When f=0.5 kHz, VR=1.3, I=1.31mA and when f=6 kHz VR=3.8 I=3.83mA

On the table 2 seeing that as the frequency increases the ZT decreases. When f=0.5 kHz ZT= 3.06kΩ and when f=4 KHz ZT=1.1KΩ

At very low frequencies the capacitive reactance will be quite large compared to the series resistive element and the network will be primarily capacitive in nature. On the table 3 seeing that when f=0.2 KHz Xc=13.21KΩ θ=-85.7 and when f=10KHz Xc=78.32Ω θ=-4.5

Error Analysis

On the table 2 seeing that there is a small difference between the two formulas of ZT. When f=6 KHz ZT=1.04kΩ and ZT=1.02kΩ. The difference is very small and you can calculate by: difference%= (ZT-ZT)/ZTx100%

Ex (1.04-1.02 )/ 1.04 x 100% = 1.9% difference.

RECOMMENDATIONS

The voltage across the capacitor becomes shorter with increasing frequency since the capacitive reactance is inversely proportional to the applied frequency.

Since the voltage and current of the resistor continue to be related by the fixed resistant value, the shapes of their curves versus frequency will have the same characteristics.

The voltages across the element an ac circuit are rector-ally related otherwise, the voltage readings may appear to be totally incorrect and not satisfy KVL.

At very low frequencies the capacitive reactance will be quite large compared to the series resistive element and the network will be primarily capacitive in nature.